This paper examines the convergence of infant mortality rates across Indian states. IMR is a critical indicator of both child health and regional development. Understanding IMR convergence is vital, as it reveals whether disparities in child health are narrowing, which is essential for achieving equitable development. The findings show an absence of overall convergence of IMR across Indian states. Instead, we identify club convergence, where states with similar IMR levels cluster together, leading to widening regional disparities. States with initially low IMRs improve more rapidly, reinforcing the “Matthew effect,” while high IMR states lag behind. This pattern is also observed in neonatal and post-neonatal mortality rates. These results suggest that targeted policy interventions are necessary to address regional health inequities, with a focus on supporting lagging states to accelerate improvements in child health outcomes.